DQN input representation for a card game
120 inputs can be handled by a complex enough network. Dealing with high complexity is one of NN's strengths.

Using a (120,) vector or a (3,40) matrix is the same, they're still 120 inputs. Your binary encoding should work. Another option is a single (40,) vector, with 0 being "still in deck", 1 being "in hand", 2 being "on table", 3 being "already played". 

If the types of cards are irrelevant, you could actually have a (3,10) matrix with counters of cards (1 in hand, 1 in table, 2 already played). You can try different approaches and see what works best.